If you've got a mattress that's too soft then yes, sleeping on the floor can help. I actually got a big sheet of plywood and put it on top of my mattress, under the sheet, and that helped (I've now bought a much firmer mattress so I don't need the plywood anymore).
As jenstar says, if you're sleeping on a mattress that is too soft and doesn't support your spine, a period of sleeping on the floor might help although it might be a little uncomfortable. . But the main query is: What is causing your bad back? Is it poor posture? Do you sit too long at a computer? Is your spine kinked or misaligned to one side (possibly as a result of continually carrying a heavy bag on one shoulders? Are you suffering from a prolapsed disc which is putting pressure on a spinal nerve? One way of improving matters is to get a good book of exercises for the back (or research something on the internet) and do them religiously night and morning for a few weeks. Or possibly joining a Pilates class or something similar.
hi, suffered with bad back for many years, then had acupuncture, gave up a strenuous job and bought a new very hard bed. back pain went, unfortunately don't know which cured it, but the old bed was one where you just sank into it, so comfortable, but may well have been the problem. I would say forget the floor, get a really firm mattress.
alf.